Distance traveled by random walkers before absorption in a random medium

We consider the penetration length $l$ of random walkers diffusing in a medium of perfect or imperfect absorbers of number density $\rho$. We solve this problem on a lattice and in the continuum in all dimensions $D$, by means of a mean-field renormalization group. For a homogeneous system in $D>2$, we find that $l\sim \max(\xi,\rho^{-1/2})$, where $\xi$ is the absorber density correlation length. The cases of D=1 and D=2 are also treated. In the presence of long-range correlations, we estimate the temporal decay of the density of random walkers not yet absorbed. These results are illustrated by exactly solvable toy models, and extensive numerical simulations on directed percolation, where the absorbers are the active sites. Finally, we discuss the implications of our results for diffusion limited aggregation (DLA), and we propose a more effective method to measure $l$ in DLA clusters.Comment: Final version: also considers the case of imperfect absorber

Classical magnetotransport of inhomogeneous conductors

We present a model of magnetotransport of inhomogeneous conductors based on an array of coupled four-terminal elements. We show that this model generically yields non-saturating magnetoresistance at large fields. We also discuss how this approach simplifies finite-element analysis of bulk inhomogeneous semiconductors in complex geometries. We argue that this is an explanation of the observed non-saturating magnetoresistance in silver chalcogenides and potentially in other disordered conductors. Our method may be used to design the magnetoresistive response of a microfabricated array.Comment: 12 pages, 13 figures. Minor typos correcte

Kinetics of diffusion-limited catalytically-activated reactions: An extension of the Wilemski-Fixman approach

We study kinetics of diffusion-limited catalytically-activated $A + B \to B$ reactions taking place in three dimensional systems, in which an annihilation of diffusive $A$ particles by diffusive traps $B$ may happen only if the encounter of an $A$ with any of the $B$s happens within a special catalytic subvolumen, these subvolumens being immobile and uniformly distributed within the reaction bath. Suitably extending the classical approach of Wilemski and Fixman (G. Wilemski and M. Fixman, J. Chem. Phys. \textbf{58}:4009, 1973) to such three-molecular diffusion-limited reactions, we calculate analytically an effective reaction constant and show that it comprises several terms associated with the residence and joint residence times of Brownian paths in finite domains. The effective reaction constant exhibits a non-trivial dependence on the reaction radii, the mean density of catalytic subvolumens and particles' diffusion coefficients. Finally, we discuss the fluctuation-induced kinetic behavior in such systems.Comment: To appear in J. Chem. Phy

Anomalous temperature behavior of resistivity in lightly doped manganites around a metal-insulator phase transition

An unusual temperature and concentration behavior of resistivity in $La_{0.7}Ca_{0.3}Mn_{1-x}Cu_xO_3$ has been observed at slight $Cu$ doping ($0\leq x \leq 0.05$). Namely, introduction of copper results in a splitting of the resistivity maximum around a metal-insulator transition temperature $T_0(x)$ into two differently evolving peaks. Unlike the original $Cu$-free maximum which steadily increases with doping, the second (satellite) peak remains virtually unchanged for $x<x_c$, increases for $x\ge x_c$ and finally disappears at $x_m\simeq 2x_c$ with $x_c\simeq 0.03$. The observed phenomenon is thought to arise from competition between substitution induced strengthening of potential barriers (which hamper the charge hopping between neighboring $Mn$ sites) and weakening of carrier's kinetic energy. The data are well fitted assuming a nonthermal tunneling conductivity theory with randomly distributed hopping sites.Comment: 10 REVTEX pages, 2 PostScript figures (epsf.sty); to be published in JETP Letter

Non-saturating magnetoresistance of inhomogeneous conductors: comparison of experiment and simulation

The silver chalcogenides provide a striking example of the benefits of imperfection. Nanothreads of excess silver cause distortions in the current flow that yield a linear and non-saturating transverse magnetoresistance (MR). Associated with the large and positive MR is a negative longitudinal MR. The longitudinal MR only occurs in the three-dimensional limit and thereby permits the determination of a characteristic length scale set by the spatial inhomogeneity. We find that this fundamental inhomogeneity length can be as large as ten microns. Systematic measurements of the diagonal and off-diagonal components of the resistivity tensor in various sample geometries show clear evidence of the distorted current paths posited in theoretical simulations. We use a random resistor network model to fit the linear MR, and expand it from two to three dimensions to depict current distortions in the third (thickness) dimension. When compared directly to experiments on Ag$_{2\pm\delta}$Se and Ag$_{2\pm\delta}$Te, in magnetic fields up to 55 T, the model identifies conductivity fluctuations due to macroscopic inhomogeneities as the underlying physical mechanism. It also accounts reasonably quantitatively for the various components of the resistivity tensor observed in the experiments.Comment: 10 pages, 7 figure

Phase coherence in tight-binding models with nonrandom long-range hopping

The density of states, even for a perfectly ordered tight-binding model, can exhibit a tail-like feature at the top of the band, provided the hopping integral falls off in space slowly enough. We apply the coherent potential approximation to study the eigenstates of a tight-binding Hamiltonian with uncorrelated diagonal disorder and long-range hopping, falling off as a power mu of the intersite distance. For a certain interval of hopping-range exponent mu, we show that the phase-coherence length is infinite for the outermost state of the tail, irrespectively of the strength of disorder. Such an anomalous feature can be explained by the smallness of the phase-space volume for the disorder scattering from this state. As an application of the theory, we mention that ballistic regime can be realized for Frenkel excitons in two-dimensional molecular aggregates, affecting to a large extent the optical response and energy transport

Intensification of vibration mixing of particulate solids by means of multi-layer loading of components

International audienceThe objective of the study is to show how initial distribution of dissimilar particulate components influences the mixing time and mixture quality. The dissimilar components have a tendency to segregate in one another, and it is impossible to achieve the perfect mixture of them in industrial settings. Nevertheless, the situation can be improved if the components are loaded as a sequence of several sandwiches, each of these sandwiches containing layers of components that are proportional to their share in the mixture. In this case, a sort of pre-mixing occurs while still at the loading stage – which allows reducing the optimum mixing time and increasing the homogeneity of the mixture. The theory of Markov chains was used to simulate the mixing kinetics. It is shown that the number of loaded sandwiches has a very strong influence on the process efficiency. A loading device that can effectively realize multi-layer loading is proposed. The mixing kinetics for ternary mixture of glass beads was investigated experimentally at a lab scale vibration mixer. A one-time loading and a two-sandwich loading were compared. It was shown that the optimum mixing time and non-homogeneity of the mixture were reduced by half in the latter case

A Markov chain model of mixing kinetics for ternary mixture of dissimilar particulate solids

International audienceThis paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov chain model is proposed to describe the process. At each time step, the exchange of particulate solids between the cells of the chain is divided into two virtual stages. The first is pure stochastic mixing accompanied by downward segregation. Upon the completion of this stage, some of the cells appear to be overfilled with the mixture, while others appear to have a void space. The second stage is related to upward segregation. Components from the overfilled cells fill the upper cells (those with the void space) according to the proposed algorithm. The degree of non-homogeneity in the mixture (the standard deviation) is calculated at each time step, which allows the mixing kinetics to be described. The optimum mixing time is found to provide the maximum homogeneity in the ternary mixture. However, this ``common'' time differs from the optimum mixing times for individual components. The model is verified using a lab-scale vibration vessel, and a reasonable correlation between the calculated and experimental data is obtained.(C) 2016 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved

ТЕОРЕТИЧЕСКИЙ ПОИСК ОПТИМАЛЬНОЙ ЗАГРУЗКИ ПЕРИОДИЧЕСКОГО СМЕСИТЕЛЯ ДИСПЕРСНЫХ МАТЕРИАЛОВ

International audienceThe objective of the study is to investigate how the hold-up of particulate solids to be mixed in a batch mixer influences the mixture quality and mixer capacity. It is known that a small amount of components (i.e., a small hold-up) allows reaching better quality of a mixer but leads to small capacity of a mixer. It is particularly appreciably when it is necessary to mix the components, which have a strong tendency to segregate into each other. In this case the perfect mixture cannot be reached, and there exists the optimum mixing time, at which the mixture homogeneity reaches maximum. This optimum time increases with the hold-up increase. Thus, from the mixing as such viewpoint, it is better to mix components not in big portions one time but in small portions several times. However, the total time of a mixing process consists of the loading time, mixing time and discharge time. The loading time depends on many factors such as a dosage device design, feeders design, and others, while the discharge time is usually much smaller. Thus, the mixer capacity is determined not only by the mixing time but also by the loading time at least. In order to estimate the mixer capacity at a required mixture quality, a cell model based on the theory of Markov chains is used. It is shown that the optimum hold-up exists that provides the maximum mixer capacity, and tЦель настоящего исследования – выявить, как загрузка предназначенных для смешивания в периодическом смесителе дисперсных материалов влияет на качество смеси и производительность смесителя. Известно, что небольшие количества компонентов (то есть малая загрузка) позволяют обеспечить лучшее качество смеси, но приводят к меньшей производительности смесителя. Особенно это проявляется, когда необходимо смешать компоненты, склонные к значительной сегрегации друг в друге. В этом случае полностью однородная смесь вообще недостижима, и существует оптимальное время смешивания, при котором качество смеси достигает максимума. Это оптимальное время возрастает с ростом загрузки. Таким образом, с точки зрения собственно смешивания, предпочтительно смешивать компоненты не один раз большими порциями, а несколько раз малыми порциями. Однако, полное время процесса смешивания состоит из времени загрузки смесителя, времени собственно перемешивания и времени разгрузки. Таким образом, производительность смесителя определяется не только временем собственно перемешивания, но также, по меньшей мере, и временем загрузки. Для того, чтобы оценить производительность смесителя при заданном качестве смеси, использована ячеечная модель, основанная на теории цепей Маркова. Показано, что существует оптимальная загрузка, которая обеспечивает максимальную производительность смесителя, и эта оптимальная загрузка существенно зависит от времени загрузки компонентов